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import random
class CommitmentScheme(object):
def __init__(self, oneWayPermutation, hardcorePredicate, securityParameter):
'''
oneWayPermutation: int -> int
hardcorePredicate: int -> {0, 1}
'''
self.oneWayPermutation = oneWayPermutation
self.hardcorePredicate = hardcorePredicate
self.securityParameter = securityParameter
# a random string of length `self.securityParameter` used only once per commitment
self.secret = self.generateSecret()
def generateSecret(self):
raise NotImplemented
def commit(self, x):
raise NotImplemented
def reveal(self):
return self.secret
class BBSBitCommitmentScheme(CommitmentScheme):
def generateSecret(self):
# the secret is a random quadratic residue
self.secret = self.oneWayPermutation(random.getrandbits(self.securityParameter))
return self.secret
def commit(self, bit):
unguessableBit = self.hardcorePredicate(self.secret)
return (
self.oneWayPermutation(self.secret),
unguessableBit ^ bit, # python xor
)
class BBSBitCommitmentVerifier(object):
def __init__(self, oneWayPermutation, hardcorePredicate):
self.oneWayPermutation = oneWayPermutation
self.hardcorePredicate = hardcorePredicate
def verify(self, securityString, claimedCommitment):
trueBit = self.decode(securityString, claimedCommitment)
unguessableBit = self.hardcorePredicate(securityString) # wasteful, whatever
return claimedCommitment == (
self.oneWayPermutation(securityString),
unguessableBit ^ trueBit, # python xor
)
def decode(self, securityString, claimedCommitment):
unguessableBit = self.hardcorePredicate(securityString)
return claimedCommitment[1] ^ unguessableBit
class BBSIntCommitmentScheme(CommitmentScheme):
def __init__(self, numBits, oneWayPermutation, hardcorePredicate, securityParameter=512):
'''
A commitment scheme for integers of a prespecified length `numBits`. Applies the
bit commitment scheme to each bit independently.
'''
self.schemes = [BBSBitCommitmentScheme(oneWayPermutation, hardcorePredicate, securityParameter)
for _ in range(numBits)]
super().__init__(oneWayPermutation, hardcorePredicate, securityParameter)
def generateSecret(self):
self.secret = [x.secret for x in self.schemes]
return self.secret
def commit(self, integer):
# first pad bits to desired length
integer = bin(integer)[2:].zfill(len(self.schemes))
bits = [int(bit) for bit in integer]
return [scheme.commit(bit) for scheme, bit in zip(self.schemes, bits)]
class BBSIntCommitmentVerifier(object):
def __init__(self, numBits, oneWayPermutation, hardcorePredicate):
self.verifiers = [BBSBitCommitmentVerifier(oneWayPermutation, hardcorePredicate)
for _ in range(numBits)]
def decodeBits(self, secrets, bitCommitments):
return [v.decode(secret, commitment) for (v, secret, commitment) in
zip(self.verifiers, secrets, bitCommitments)]
def verify(self, secrets, bitCommitments):
return all(
bitVerifier.verify(secret, commitment)
for (bitVerifier, secret, commitment) in
zip(self.verifiers, secrets, bitCommitments)
)
def decode(self, secrets, bitCommitments):
decodedBits = self.decodeBits(secrets, bitCommitments)
return int(''.join(str(bit) for bit in decodedBits), 2)
if __name__ == "__main__":
import blum_blum_shub
securityParameter = 10
oneWayPerm = blum_blum_shub.blum_blum_shub(securityParameter)
hardcorePred = blum_blum_shub.parity
print('Bit commitment')
scheme = BBSBitCommitmentScheme(oneWayPerm, hardcorePred, securityParameter)
verifier = BBSBitCommitmentVerifier(oneWayPerm, hardcorePred)
for _ in range(10):
bit = random.choice([0, 1])
commitment = scheme.commit(bit)
secret = scheme.reveal()
trueBit = verifier.decode(secret, commitment)
valid = verifier.verify(secret, commitment)
print('{} == {}? {}; {} {}'.format(bit, trueBit, valid, secret, commitment))
print('Int commitment')
scheme = BBSIntCommitmentScheme(10, oneWayPerm, hardcorePred)
verifier = BBSIntCommitmentVerifier(10, oneWayPerm, hardcorePred)
choices = list(range(1024))
for _ in range(10):
theInt = random.choice(choices)
commitments = scheme.commit(theInt)
secrets = scheme.reveal()
trueInt = verifier.decode(secrets, commitments)
valid = verifier.verify(secrets, commitments)
print('{} == {}? {}; {} {}'.format(theInt, trueInt, valid, secrets, commitments))
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